Question 61. At x = 0.5, the polynomial x2(1-x)2 has

Question 62. Given that v is a vector field and f is a scalar field, match the equations in Group I with their
physical meaning in Group IIGroup I                         Group IIP. div (v) = 0                 1 . I r r otationalQ. curl (grad(f)) = 0     2 . IncompressibleR. div (grad(f)) = 0       3 . PotentialS. v = grad(f)                4 . Laplace equation

Question 63. The temperature field of a slab is given by T = 400 - 50z exp(-t - x2 - y2). The temperature gradient in y-direction is

Question 64. Match the principles given in Group I with corresponding corrosion terminology in Group IIGroup I                                   Group IIP. Electrode polarization 1. DezincificationQ. Passivity                      2. Intergranular attackR. Selective leaching         3. Over voltageS. Grain boundary precipitation 4. Surface oxide film

Question 65. What does the solution of the following ordinary differential equation represent?y dy/dx + x = 0

Question 66. Identify the correct combination of the following statements P. Hydrogen electrode is a standard used to measure redox potentials Q. Activation polarization refers to electrochemical processes controlled by reaction sequence at
metal-solution interface R. Potential-pH diagrams can be used to predict corrosion rates of metals S. Cathodic protection can use sacrificial anodes such as magnesium

Question 67. Consider a reaction with activation energy of 8.314 kJ/mol that takes place at 300 K. If the reaction
rate is to be tripled, the temperature of the reaction should be

Question 68. Match the processes in Group I with the objectives in Group IIGroup I                              Group IIP. Vacuum Arc Degassing (VAD) 1. Primary iron makingQ. LD                           2. Secondary steel makingR. COREX                    3. Direct smeltingS. Blast Furnace        4. Primary steel making

Question 69. The reduction of FeO with CO gas in co-current flow is given by the following equation: FeO + CO = Fe + CO2            ∆Go = 8120 J at 1173 K The ratio of pCO/pCO2 for this reaction at 1173 K is

Question 70. The sulphide capacity (CS) of liquid slag of composition 55 wt.% CaO, 20 wt.% SiO2, 5 wt.%
Al2O3, and 10 wt.% MgO is given by the following equationlog CS = 3.44 (XCaO + 0.1 XMgO - 0.8 XAl2O3 - XSiO2) - (9894/T) + 2.05 where, X is mole fraction of the respective components. Atomic weights of Ca, Mg, Si, Al and O are 40, 24, 28, 27 and 16 respectively. The value of CS at 1900 K is